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Full text of "Column and plate compressive strengths of aircraft structural materials 24S-T aluminum-alloy sheet"

V^cAl-IIO 



AEE No. L5F01 



1 



NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS 
If 



WARTIME REPORT 

ORIGINALLY ISSUED 

June I9U5 as 
Advance Has trie ted Beport L5FOI 



COLUMN AND PLATE COMPEESSIVE STRENGTHS 

OF AIRCRAFT STRUCTURAL MATERIAI£ 

2l^S-T ALUMINUM- ALLOY SHEET 

By Eugene E. Lundquist, Evan H, Schuette, 
George J. Heimerl, and J. Albert Ro/ 

Langley Memorial Aeronautical Laboratory 
Langley Field, Ya. 

UNtVERSlTY OF FLOPiDA 

DOCUMENTS DEPARTMENT 

1 20 MARSTON SCIENCE LIBRARY k 

P.O. BOX 117011 

GAINESVILLE, FL 32611-7011 USA 




WASHINGTON 

NAC A WARTIME REPORTS are reprints of papers originaUy issued to provide rapid distribution of 
advance research results to an authorized group requiring them for the war effort. They were pre- 
viously held under a security status but are now unclassified. Some of these reports were not tech- 
nically edited. All have been reproduced without change in order to expedite general distribution. 

L - 190 



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\-x3 y^'? ^'^'^ •?sO*^7^ 1 



NAG A A.^R No. L^FOl 

NATIONAL ADVISORY COMMITTEE FOR /iERONAUTICS 



ADVA^IGE RESTRICTED -JEPORT 



COLUMI AND PLATE COMPRESSIVE STRENGTHS 
OF AIRGR/iFT STRUG TUR..L MATERIALS 

2I4.S-T ALUMINUM- ALLOY SHEET 

By Eugene E. Lundquist, Evan H. Schuette 
George J. Heimerl, and J. Albert Roy 

SIJIViMARY 



Column and plate compressive strengths of 2lj.S-T alu- 
minum-alloy sheet were determined both within and beyond 
the elastic r^nge from tests of thin-strip columns and 
from local-instability tests of formtad 2- and channel- 
section columns. These tests are the first of a series 
in an extensive research investigation to provide data 
on the structural strength of various aircraft m.aterials. 
The results, which are pre>-ente5. in the form of curves 
and charts that may be used in the design and analysis 
of aircraft structures, supersede preliminary results 
published previousl^f. 



INTRODUCTION 



Column and plate members in an aircraft structure are 
the basic elements that fail by instability. If efficient 
structures are to be designed, the strength of these ele- 
ments must be known for the various aircraft materials. 
Aji extensive research program has therefore been under- 
taken at the Langley Memorial Aeronautical Laboratory to 
..establish the column and plate compressive strengths for 
a number of the alloys available for use in aircraft 
structures. Reliable and rapid pi-'ocedures for testing 
such matei'isls have already been developed and are 
described in referencjes 1 and 2. 

The first m.aterlal tested during the present investi- 
gation was 2[t.3-T aluminum- alloy sheot. The results for 
this material, given herein, supersede those contained 
In a preliminary report (reference 2). 



2 NAG A ARR No. L^FOl 

SYMBOLS 

L length of column 

p rr^dius of gyrstion 

c fixity coefficient used in Suler column formula 

— p effective slenderne^s I'-atio of thin-stx-'io column 
p^fc 

b width of piste 

brp width of flfinge of Z- or channel section (see fig. 1) 

b™ width of web of Z- or channel section (see fig. 1) 

r inside radius of bend of Z- or channel section 
(see fig. 1) 

t thickness of pl-^te 

k nondimensional coeffj.cient used in plate-buckling 
formula 

k^ coefficient k used with bjy- pjid t in plate - 
buckling formula (see fig. 2 and reference 3) 

Sq modulus of elasticity in comoression, taken as 
10,700 ksi for ^i+S-T aluminum alloy 

T nondimensional coefficient for columns (The value of 
T is so determined that when the effective 
modulus TE(, is substituted for En in the 
equation for elastic buckling of columns, the 
computed critical stress agrees with the 
experimentally observed value. The coefficient t 
is equal to unity within the elastic range and 
decreases with Increasing stress beyond the elastic 
range. ) 

r\ nondimensional coefficient for plates corresponding 

to T for colu:nns 

|j, Pois son's ratio, taken as O.3 for 2[|.S-T alumlniun alloy 



NAG A AR'R No. L5F01 



^ Q-p criticsl coiTiprsssive stress 

<7^„„ sver^ee comoressiva stress at inaximurn load 

o compressive yisld stress 

]\STHODS OP TESTING M3D ANALYSIS 

All tests were irisde in hydraulic testing machines 
accurate to within three-fourths of 1 percent. The ends 
of the stress-strain specimens and the colunins were ground 
flat end square. 

Stress-stra in curves .- The compressive stress-strain 
data, which identify the material for correlation v/ith 
its column and plate compressive strengths, were obtained 
from tests of single -thickness sceclinens in a compression 
fixture of the Montgomery-Temp lin type shovm in figure 5' 
This fixture v/as used only for flat compression specimens, 
which represented the material before forming. Infor- 
mation on the teclinique used in maklnn these tests is 
presented in reference Ij.. For the bent material in the 
corners of the formed Z- and channel sections, compression 
specimens were cut from^ the corner portion and tested in 
the special fixture shoivn in figure k. 

Column strength. - The column strength and the asso- 
ciated effective column modulus were obtained by testing 
thin-strip columns of the m^aterial with the ends clamped 
in fixtures of the type shown in figure 5. The use of 
end fixtures of this type is discussed in detail in 
reference 1. The fixtures used have been improved, and the 
method of analysis has been modified since the publication 
of reference 1. The method now used results in a columji 
curve representative of nearly perfect column specimens. 
In addition, the miethod now takes into account the fact 
that columns of the dimensions tested are actually plates 
with two free edges. 

Plate compressi ve stre ngcii.- The plate compressive 
strength of 'the material was obtained from compression 
tests on Z- and channel-section columns so proportioned 
as to develop local instability, that is, instability of 
the plate elements of which they are comiprised. (See 
fig. 6.) Inasmuch as the flanges and webs of such columns 
are in reality plates with various ■ kinds of edge suoport. 



i| KAGA ARR No. L5?01 



the problem cf Iccel instability of these colur.ms Is a 
plete-buckllng pi'obleiii, aiicl tiie plate compressive strength 
of the ..ripterlal wss evsluated frcm these tests. The 
lengtlis of the colurniis were so chosen as to avoid colunxi 
faiiui'e and still provide satlsf actoi^y local- Inatfbllity 
data. These conslderptious ere discussed in reference 5» 

The Z- and chaiinel-section cclanms were tested v/ith 
the ends bearing directly agginst the testing-machine 
heads, which were carefully alined to insure uniform 
bearing on the colamia ends. A Z-section colioirji urider 
test is shov.n in figure 7« Th'- relative displacemencs of 
pointers, which 'vvera supported by extension arms attached 
to the fl-snges of the specimens, were measiared by the 
cpticfl -Tiicroirietyrs thet can bo seen in figure 7* Ttie 
displacement was taken as a measure of the cross-sectional 
distoi'tion, and the critical compressive stress was obtained 
from stress-distortion curves of the type illustrated in 
figure 3, The critical stress y»as determined as the 
stress at the point near the top of the iaiee of the stress- 
distortion curve at vjhich a marked increase in distortion 
first occurred w3 th sm.all increase in stress. (See fig. 3.) 



RESULTS AJTD DISCXjSSIOK 



Because the compressive properties of aluminxxm-alloy 
sheet may vary appreciabl;/ , the data and charts of the 
present report should not be applied to the desifxi of 
structures of 2IlS-T aluminum- allov sheet having compressive 
properties appreciably different from those reported 
herein unless a suitable method is devised for adjusting 
test x'-esalts to account for variations in material 
properties. 



Compressive Stress-Strain Curves 

Com.pressive stress-strain curves obtained for tne 
flat sheet material used in marine; the colui:Xi3 are given 
in figure Q for both directions of grain. The Z-, channel, 
or thin-strip colutmis to which a particular stress-strain 
curve applies are indicated in table 1, to^^ether with the 
value of the coiiipressive yield stress CJ^^. for that stresS' 

strain curve. These values average approximately i|Ij. ksi 
for the flat sheet material in the v/ith-grrdn direction 



NAG A ARR No. L5F01 5 

and Ij.9 Ksl in the cross -grain direction. The modulus of 
elasticity in compression v/as taken as 10,700 ksi, the 
accepted value for 2lj.S-T aluminum alloy. 

When the flat sheet mrterial is bent to an inside 
radius r of Jt to form a Z or channel, the cold vifork 
done on the material evidently raises the compressive 
yield stress for the curved corner portion above that for 
the flat web or flange, about lei percent for the with- 
grain and 10 percent for the cross-grain direction. (See 
fig. 10. ) Because the curved corner specimens included 
along their edges some flat material (about 1^.0 percent 
of the total area) for which the yield stress is lower 
than that for the curved portion, the actual increase in 
the compressive yield stress for the corner portion may 
be scir-ewhat greater than the Increase indicated in fig- 
ure 10. The important result to note is that the com- 
pressive properties of a formed section may not be uniform 
over the cross section. 



Col^ormi Stz-'ength 

The results of the tests of the thin-strip columns 
are given by the coluinn curves of figure 11 for the two 
directions of grain. 

At stresses beyond the elastic range, the experi- 
mental values of a^^^ are lov/er than those computed by 
the Euler column formula (see elastic-buckling curve, 
fig. 11), because of the I'eduction in the effective 
modulus of elasticity. The effective modulus to be 
substituted for E^ in the Euler coluirm formula to bring 

calculatsd and experimental values of o^^ into agreement 

is givexi as tEc where t Is a coefficient that is equal 
tc unity in the elastic range and decreases with Increasing 
stress beyond the elastic range. In structural calculations 
in vifhlch it is impossible to use directly values obtained 
from the column curve (fig. 11), the value of t for a 
given stress must be known. The variation of t with 
stress for columns is therefore showi in figure 12 for 
both directions of grain. 



D 



NACA ARR Uo. LSFOl 



Fl?fcF> ComnressT ve 3tren.2;th 



The i-esults o'f ths local-instability tests of the 
forined Z- rnd chaixne 3 -section col''aiiii"s , used to determine 
the plate compressive strength, ar'e Piver. in tables 2 
and 5. The important ralationcbips for corr.pressed platos 
obtained from these testr are sho«vn on the curves ajid 
design charts presented in the follov.'in^ paragraohs. 

Plate-buck] ing c urve . - The plate-buckling curve, 
which is analo.:ous to the colur::n .curve , is shovm in fig- 
ure 15 for olstes loaded in the wlth-grain direction. 
The abscissa Ir figure I3 is suggested by transposing the 
plate-buckling equation 



cr 



krr^^t- 



12(l-i..^)b' 



(1) 



to the form 



a. 



cr 



TT^Hl, 



----|2 



(2) 



whore the subscript W is added to r.aice the terms b 
and k of the equation correspond to the entries in 
tables 2 smd 5« The siir.ilarity between the form of 
equation (2) .and the follovv'lng form of the 3uler colur.xi 
for.iuls 1? to be noted: 



cr 



■J 

C 

Vp,v 



(5) 



At stresses bejor.d the elastic range, as in the case 
cf colii/iins, the experimental values of Q for plates 

are lovvex* than those given by equation (2) for clastic 
buck]. ing (see elastic-bucicling curve, fig. 15), because 
of the reduction in the effective modulus of elasticity. 
The effective plate modulus corresoonding to tS_ for 

columns is rlv-n as rS 



c» 



rnd the varlftion ol 



c 
r 



th 



NACA ARR No. L5FOI ( 

stress is given, togethex" with the variation of t, in 
figure 12. The crossing of tne t_ and r:-curves shown 
in figure 12 occurs because the formed columns apparently 
had an appreciable degree of imperfection, which resulted 
in the deviation of the r,- curve from unity at a lower 
stress than that at which th3 T-curve, reoresentative 
of nearly perfect columns, deviates from unity. 

Relationshio of a to o_„/n for plates.- In 



cr cr 




problems concerned with the strength of plates, it is 
sometimes desirable to insert the value of nS^ for E^ 

in the plate-buckling formula, equation (1), and to write 
the eqiistion in the transposed form 



('-^) 



In this form the v?lue of "^cr/^^ ^-'^ given by the modulus 
of elasticity, Poisson's ratio, the ji.eometric dimensions 
of the elate, and the coefficient Ic, The value of a^^ 

can then be obtplned by use of the curve of o^^ against 
o^-p/v given in figure l!|. This curve m.ay be obtained by 
plottinT the data directly or by plotting from the faired 
curves of figure 15. 

As in the case of equation (1), the subscripts W 
may be added to k end b of equation (I).), and ^cr^''^' 
m.ay be determined for a Z- or channel-section by the use 
of the formula and curve of figure 2. 

Maximum compressive strength of plate elements . - In 
the case of a plate loaded in long i tud in a 1 c ompre s s i on , 
the supported, or restrained and supported, side edges 
remain essentially straight after buckling and ore capable 
of carrying additional load. As a consequence, there is 
a 'maximum strength for the plate that is greater than 
the buckling strength. 

Theoreticrl studies that appear in the literature 
concerning the ultimate strength of plates and the asso- 
ciated effective width of the plates after buckling 
indicate that the average stress at miaxiraum load is 
related to the critical stress. It is therefore reason- 
able to assum.e that the average stress at maximmn loed 



8 FACA .Al^R No. L5FOI 



a„, „^ for tli-^ co'.nbinatiori of "olgte elsL-'ents that ms-ke up 

the 2- or chc'<rinel-sec tloii oolu.ia 11 slso related to tho 
criticril str^ess for the ccmbinstlori . Accoriingly, tns 
e.xeri:-.ner,t£l veluos obtcvinad era plotted in figure I5 
as o^.^ sgap'nst the r.9t:*o ^cr/^r:irx5 ^nd from thi:; ^^S~ 
ure a definite ralptior:ship ii s 3e:. to exist between 
o^r, and '^r.iax ^-^ ^ given ve-lu3 of by;/t. 

In corra c?S3F. , vcl.ies of "j.v.p;. r ether thsn ^cr 
may be requi^-'ed in strength c£-lcalption:; . fj-.e values of 
a.--^gy are therefore plotted against ^crA) ^^' ^'ifc^ii'"- 16. 
The fe3sibility of making such a plot is indicated by the 
rel.atlorshio bet'Ji/een o^v, aiid '^oxv'V shovVi'i in fii^ure 1I4. 
and the I'elaticnship betv:een a.jia" ^^'^'^ "^cr sbo'Vn in 
fiprure 15 . Figure 16 is i?articulsrlv useful because tne 
qumitiby '^cr/''^ ^*-^ doterrninod by Imomi quantities 
a-^cordlng to the fori!;ula fnd cur/-3 of figure 2. 

The ressc-n for the diff^vrence in the curves of fig- 
ures 15 and 16 for difTorent values of b.. /t is not 

fiilly uTiderstocd. Tro s tress-str ■oa.n curves hi-ve indicated, 
nowever^ that the bevidlng of the naterial in the for:r.ing 
of the colunns raises the compressive yield stress for the 
ma^'erial in tiie corners. ( 3ee fig. 10.) An exeunination 
of the data Gliowed thct rs b'..-/t :s reduced for a given 
thickness t and a given value of c^cr/hj the total cross- 
sectional ax'^ea is also redj.ced; the fixed area of high- 
strength tent matei'isl in the corners therefoi-e becoT.es a 
higher rercentage of the total eres. This fact .may account 
for the hi;Ther values of a^ax obtained at given values 
of '^crAl '^''•*' "t-^'"^ Z- and cnannsl-section columns 'vith 
lo'.ver values of b-j/t. (See fig, 16.) 

Zf fee t of gr a i n d i ^0 c 1 1 on on plate s t r en .c t h . - The 
data on plate strength '^rssen ted in figures IJ to lo were 
obtained from columns loaded in the wibh-grain direction. 
In order to deter^:ine_the effect of grain direction on the 
values of o^r' f^'id ^v.ax» a ^'sw coliAjmas were constructed 
pj.id tested with the grain of the sheet at right angles 
to the axis of the col'jurji. These columns are herein 
designated cross -gr fin columns. 

In figurot. I7 and 1,,., th^ aata obtained from the 
cross-grain columns are plotted as exoer-mental joints 



NACA AP.Vx Ho. L5F01 9 

for comparison with curves taken from figures iL. snd l6 

for the with-grain colioinns. Only at the higher stresses, 

where the stress-strain curva i'or the cross-grain direction 

differs noticeably from tne stress-strain curve for_the 

with-srain direction, are the values of o and a „„,, 

' cr max 

greater for the cross-grain columns than for the with-grain 

columns. The average increase in the high-stress region 

was about I4. percent for o and about 2 percent for '^rpax' 

vifhereas the cross-grain compressive yield stress was approx- 
imately 11 percent greater than the with-grain compressive 
yield stress. 

Ch. arts f o r loc a 1 in s t^ab i lity of Z- aj:;d channel-section 
columns.- Th.e olaFe~compre"ssive strength of the materi al 
was evplu^ted from tests of Z- and channel-section columns. 
The results of these tests, which provided this information 
regarding olates, may also be applied directly to formed 
Z- and channel-section col'Jini:i3 that fail by local insta- 
bility. These results can be conveniently sujuraarized in 
the form of charts that give directly, in terins of the 
dimension ratios bp/b;sr and b-,:/t, the critical stress 

and the average stress at maximum load. Such charts, 
based on the theoretical curve of figure 2 and the experi- 
m^ental data, are given in figures I9 to 21. 



COWGLUDING REMARK 



The important conclusions of this report are em.bodied 
in the test data of column and plate compressive strengths, 
which are presented in the form of curves and charts that 
may be used in the design 9nd analysis of aircraft 
structures of 2l|S-T aluminum- alloy sheet. 



Lsngley ]V-eraori?l Aaron ^^utical Lr.borat»ry 

N-'tional Advisory Comi.iittcje iov Aoronautics 
Langley Field, Va. 



13 NACA art; Y.o. I.5?01 



Lundoui=:.t, R\x::er,B E., RossjT'Sn, Csrl A., nncl Houlolt, 
JoVin G-: A Riethod. fo-' DsDei'ml/iinp- the Colurrm 
Ci;rv3 frcin Tests of Columns vrith Equal Restraints 
ai?iast Rotation cr. the Ends. iMCA Til No. ^OJ, 

heliiiPrlj George J., and Roy, ■!. AlbO'rt: ih'-elitnlnsry 
Report on Tests of 2l|.S-T Alurr.lniiiii- Alloy Coluii;ns of 
Z-, Cnrnnel, ^nd E-Seotion That Develop Locrl 
In£t?biJlty, IIA^^'A ?.3V.o. JJZ'?, lSl|5 • 

•vrollj A. C. , risiiOi^, Gordon P., and Heiirnerl, George ^ 
Charts for Cr'lcalrtion of the Critical Stress for 
Locrl Instability cf GolUinns v,ith I-, Z-, Ghsnnel, 
sna Rect£:n,!?:ui&r-Tub9 oectl-.)n. ,NACA ARR ?\^o. JKOIl, 

■9i 



1 



LL 



iSiiJ. 



Kotonchi':, Joseph lu , Woods, waiter, rnd Weinberger, 
Robert A. : InvOBtigatlcn of r.-3thods of Supporting 
S.lnj^le-lhiclcness Specimens m e. Fixture for DeterrrJ.' 
nation of Corirpre3s;ive Stress-Str^^an Curves. KAGA 
No. T,5E1S , 19': 5. 



t31 



Keimerl, George J., tnd Roy, J. Albert: Determinstion 
of Desii'pble Lengths of Z- and Chf'imel-Section 
Colunins for Locai-Instfjbility Tests. NAG A H3 
No. lIilUO, IPL4. 



MCA .-iRR No. L5F01 11 

TABLE 1.- CO!l'PRESSI"'''E PROPERTIES OF 2i|S-T ALUIvIBITOJ-ALLOY SHEET 

[e^ = 10,700 ksi] 



Co: 


.umns to whic 


h stress- strt.in 




1 Compressive yield 




curve E 


apoly 


Stress- 
strain 


ST^^aGSS^ f*lA 




■ 








Type 


Direotion 
of 
loading 


Designation 
( See tables 2 and 3) 


curve 
(fig. 9) 


iVith 

grain 

(ksi) 


Cross 
grain 
(ksi) 


Thin 


"'ith grain 


All 


A 


U2.9 


U7.9 


strip 


and cross 
grain 










Z 


'.'Vith grain 


la to 6a, 6c, 7a, 10a, 
10b, 11a to 19a, 26b, 
27a, 27c, 28a, 29a, 
31b to 32c 


B 


UU.o 


U6.e 


Z 


Vvith grain 


6b, 7t to 9, 10c, 19b 


C 


i+6.3 


51.3 






to 26a, 26c, 27b, 2et,| 










280, 29b to 31a 








Z 


Cross 

grain 


la to Uc 


D 


U3.i+ 


Ue.5 


Channel 


I'.ith grain 


1 to 6a, 7a, 8a, 9a, 
10a, 11a, 12a, 13a, 
llj-a, 15a, l6a, 17a, 
18a, 19a, 20a, 21a, 
21b, 22a, 23a, 21+^, 
25a, 27a to 28a, 2Qa, 
30a to 31a, 32a, 33a, 
5l4.a, 35a, 36a 


E 


U3.i4 


i|6.9 


Channel 


'Vith grain 


6b, 6c, 7b, 7c, 8b, 
8c, 9b, 9c, 10b, 10c, 
lib, lie, 12b, 12c, 
13 b, 13 c, lUb, li4c, 
15b, 15c, I6b, I6c, 
17b, 17c, 18b, lec, 
19b, 19c, 20b, 22b, 
23 b, 23 c, 2l;b, 2i;c, 
25b, 25c, 26a, 26b, 
28b, 29b, 29c, 31b, 
32b 


F 


Uh.3 


UQ.7 


Channel 


Vi'ith grain 


31c, 32c, 33b, 3^'C, 
3Ub, 35b, 36b. 36c 


G 


U3.9 


ii7.9 


Channel 


Cross 

grain 


la to L|.c 


D 


k3'U 

1 


US. 5 



NACA aRR No. L5F01 



12 



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rH rcNfvj jvo (M r— '<^c7^^-o^o f\J ON ^c^_:d^^ ctnono oco f-^o irNf- 
ONaNCjNr^c^-fNJ '<>c\jco cr\0_j-irvd- rH rH rH CO 0000 t^ C^LfMAJ-^j- 

rvj rvj CM HrH CM >H iHH r-t r^ rH 



r-i^o-d'CTNf-O f— r-oD '<^<3^oor^J o m i-irvjcorH ^iH h-cr\^'<v^_:j- 



cono r>- on r-cTsvo 00 J- i^Ncvi J- f<\j- 

O O O i-t r^vONO-sO r-C^f-OTCDCO 



NO l/VO O CTnOnKNCVJ \r*^ rH r-t On 

ONONONiHOOrVjrvI KNKNuTNirNj- 

rH.-lrHrHrHi-(.Hr-( r-t^ 



rH c7N^<^t--^<^^-la^ r> f-i-i KNr— r<Nip, 

<-i O "-too C7N^iOvrOvr~.t~-t — CO CTnCO 



rHiTNOOOi-tOOCO ^fVO l-H CO On 
rvj (M rv) C--t^^-'<Nf<NrH o ONcnoo 



|-r<M<Nrcvrvj rvj rvj fvj r\j rvj rH m .-i m i-i iH ih 



_:JvOrn f~-_d- ON ffNNO O K^r^ MNvO tr. 
OnOCO OOOCTnOOOOOOCJnO 
oo ONCO O crsrvj KM<\J-_:t-cl- 14^-4 "> 



CO -H 00 00 ctnno aNoo_d<D r^NO rvj 

OnOnOncTnCTnCTnOOQOOT OCT) o o 

LfNLTMrNvONONO c^ c~-oo onctno o 



NO CO r-kO t~-r— <-tooco<-» >hco <-• itn 

_:^nO LfVO KNiO C\J. ■ 



Xr^ On 



C\J_d-r-l rH iTnO ITMH CVJ OnO LfNCVJ 

rvjV^ rvj r-O rvj t^vo t^ONNO Ono 



_:±K>J-fCN^KNfVJ NNhfNrvJ rVJ rOvKNOJ 
T?v ^f^ KN KN K\^_:J_J- J-^ J- J-^ J- 



K^K^K^K^K^K^^r^K^K^(^J KNKNrvj 



OrH O rnl O O ■-< O o o o o o o o o o o o o o o o o o o o 
LrNLfNLrNirNLTNurNirM/NLrM/Na^trNLrNurN L/NtrNLrNLr\LrNtrM-rNLrNLPvLrNLp\LfNtrN 



O irNKNv_H-LrNKNKVjd-KNirNvOCO lTNKN 
rH r-\ r-{r^ »-1\OnOnO l/VO nO -.:i"^ nO 



orvIO^^'<^K^K^r<^r^o lPv^o 

\0 C — NO ITN f^ C — NO NO nO C — NO nO nO 



CD CO CO CO 00 rvirvjoji>jrvjAirvirvic\J 
iHrHrHr-irHrvjrvirvjrvjrvirvirvjojrvj 



rv)rvjrvjfvjrvj.\jc\jrvirvjrvirvjr\jr\J 
rvirvjf\jrvic\irvjrvjrvjrvjc\j-\if\jrvj 



rvj rvj r\)co t^i/NNOCo ,-\ •-{ ^^ f-LTNr— 
rvj rvj f\i LfMrvKNKNhfNcocooo rvj rvj r\j 



OOO O C~-nOnO on on rCN rvj CD KNrvi 
t^NO t~-iH fH iH ITNl/NO t-\^\r\\rs 



KN rCv rcvrcv hTN rH fH f-t iH rH r-t rVJ rvJ rvj rVJ rvl rVJ K~vrrNKNK>K 



O iTNrvjNO r<>o t--i>r\rvj o O rH_:^o 
NO i/nno ltnno trN-:tiAiA^ALrNt/Nir\UN 



rvj KNrvj irsrvj-^ti/^NONO^.nt'-' •-• 

LTNl/N lTN ITN Lf> j^ l^ LTV ^Pj l^ ^/^^ |/MJ> 



tCNr<NKNhr\h 



-^itnltm/nvo fr\vo_d"'<^t/>NO-cJ-irNurN 
oooooooooooooo 



-d- ITN irv^- ITN LrNj-_:t-dN^ -^ UNnO 

ooooooooooooo 



ax>oa)joa)43oa>43oaS43o a43ua)43oas43<(^ai43o 
f^C~-tN-CDCD CTnOncTnO O O i-H i-l rH rvj (M C\J K^^<^^r^_:i•_d■LfNl/^^^NONO 
rvj rvj rvj rvj rvj rvi f\j rvi KNr<NKNhr\»o\KN N^K^^^^K^^r^K^K^f<^N^K^^f^K^K^ 



CO 

o 

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« 43 



NACA ARR No. L5F01 



21 



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NACA ARR No. L5F01 



Fig. 1 



111 



I r= 3t 




1 



b 



W 



(I 



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r-M 



^ 



fc>w 



^ 



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NATIONAL ADVISORY 
COMMinEE FOR AERONAUTICS 



Figure!.- Cross sections <^ Z-and channel 
section columns. 



NACA ARR No. L5F01 



Fig. 2 



^W 







1 1 1 1 

/Buckling of web \ 








^ 


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restrained bv flanq 


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NATION 


L ADVISORY 


\ 
















lUMMlUtt 


UR AtRONA 


IIICS 



bp/b 



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1.0 



w 



"igure 2. -Values of k^^ for Z- and channel- section 

columns of uniform thickness (from reference 3). 

-n I2(i-ju^)bw' 



I 



i 



NACA ARR No. L5F01 



Fig. 3a, b 




V, J -^ ^- ^ 



^►^^3^,345^ »HCH 2 



(a) Unassembled. 




(b) Assembled with Tuckerman optical strain gage in 
place on specimen. 



Figure 3.- Fixture for obtaining compressive stress-strain 

curves of flat sheet. 



NACA ARR No. L5F01 



Fig. 4a, b 



r 



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^ACA ARR No. L5F01 



Fig. 5 





NACA LMAL 
40963 



....- ■^^■;.-.s.Ki,.^>ai^^....<v«^K^» 



Figure 5.- End fixtures and setup for thin-strip column tests 



NACA ARR No. L5F0] 



Fig. 5 





NATIONAL ADVISORY 
COMMinEE rOR AERONAUTICS 



Figure 6 ~ Typical cross -sectional distortion 
of columns that develop local instability. 



NACA ARR No. L5F01 



Fig. 7 




Figure 7.- Z-section column under test for study of 
instability of plates. 



NACA ARR No. L5F01 



Fig. 8 



in 
V 

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(35 

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Cross - sectional distortion 
(Pointer displocement) 



Figure 8- Illustrative stress - distortion curve for 
determination of critical stress for Jr or channel 
section colunr^ns loaded in compression . 



NACA ARR No. L5F01 



Fig. 9 



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NACA ARR No. L5F01 



Fig. 10 



60 



50 



40 






I/) 

J/) 



30 



20 



10 



Formed material from 
curved corner , 
inside radius, 3t 




h- .002 -H 



S+ra'in 



Figure 10.- Effect of forming on compressive 
stress - strain curves for 245-T aluminum - 
alloy Z- section; t =0.125 inches . 



NACA ARR No. L5F01 



Fig. 11 











i 






th grain 
Dss grain 


/ 






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NACA ARR No. L5F01 



Fig. 12 




60 



5trcs5 , ksi 



Figure \Z. - Variation of T and T] with stress for 
2.45-T aluminunn - alloy sheet, (r) obtained from 
tests of formed columns.) 



NACA ARR No. L5F01 



Fig. 13 























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^ ^ 


1 




















































































< 


5 


c 


D 


C 


D 


c 


5 , 


c 


3 


r 



^- 



o 



— >» 

"I 



o 






ee 






Diuminu 
s of for 


o 




irt 


CO 


1 


% 

-^ 


245-T 
rom te 








. M— 


o 


^^ 


> 


^- 



> o 
<j o 

~ Q 

11 

I 

^'^ 

(U (U 



d" 



I 



NACA ARR No. L5F01 



Fig. 14 



















^ 










50 




















/ 


y" 










40 










/ 


/ 






















/ 
















30 








/ 






















/ 




















20 






/ 






















/ 






















10 




/ 






















/ 
























n 


/ 














■ 











20 



40 60 

Oc/T^,k5i 



80 



100 



120 



NATIONAL AOVrSOdY 
COUMIIUE FOR AtdONAUllCS 



Figure 14.- Variation of o^^ with Ocr/r) for plates of 245-T 
aluminum- alloy sheet loaded in the with -grain direction, 
obtained from tests of formed columns -, acy= 44ksi . 



NACa ARR No. L5F01 



Fig. 15a, b 






C 




E 




3 




O 




O 




>» 




o 


c 


o 


o 


1 


"u 


F 


X QJ 


3 


g to 


C 


P m 


E 


Vr 


D 


b c 


D 


D o 




_c 


V- 


U 


1 




CO • 






^ 






-^ 




-D^ 




(U « 








to 




o 




«*^ 




U c 




^.Q 




-t— 




xO 




OO) 




E.i= 




.ip-O 




i^c 




(J — 




Dt! 




C7» 




-C 1 




■^-C 




5-t 




._5 




o 




Oa) 


S Q 




\ S 


-t- a; 
D-o 


i- 1 


V. o 


b" N 


^o 


- — » 


1 


^ 


!0 




u 




1- 




D 




CD 



b" 



NACA ARR No. L5F01 



Fig. 16a, b 














(O 








c 








E 








3 


o 




c 
o 


O 

u 




._ 




^ 




1/5 


o 




-iC 


(U 


a 


o 


^ 


in 




0) 


P" 




E 




\ 


<U 

c 


3 




D^ 


c 
o 


E 

3 


o 




JZ 

U 


"5 






^ , 


Iv 






X! 


UO 








^ 


o 






CNJ 


CM 






Formed 
.44k5i 


i 






c 


o 






«->fll 


g 






with a 
rain dir 


o 








o 

10 




C 

o 


of G 

he w 




f=r 


(U 


-t— 




\ 


iD 

1 


§-^ 


§ 


g" 


N 








5, 


>-2 



a; 

■D 

cn 



X 

o 

E 
O 



NACA ARR No. L5F01 



Fig. 17a, b 





























o 
o 

o 

« 

o 

lO 

o 
'^ 

o 

P 

8 

o 

lO 

o 
>o 

o 
'^ 

o 

fNJ 

p 


o 
_o 

E 

i 
O 

E 

liO 

>^ 

(L) 

cn 

l/l 

- ^ 
to "t/i 

P^ ° 

^ u 
si 


















C 

- c 

a 


1 








(T> 












. i 

5| r^ o ^ 




<L) 


*\ 


o" 










2 o o □ 










^i 


















s 


umns Ic 
;n from 




^ 


























H=^^ 






c 

r-1 














1/1 

e 




^^ 


to 


cn 










c 

OJ 

«^ „ 

in i^ c 

1 9^ O 




u 




\ 




^ ^ 

A ^ 




















f^ 












-mad Z 

□In cur\ 

direc+i 






















o o 
m ■"5 


o 

o 

E 


O O c 

iNJ — 


enq+hi of for 

Witti -gr 

cross -grain 


























isive str 
ections . 
or ttie 




\ 






















, .\ 


\ 
























\ 






c 
n 
















c 


\. 




cn 












irison of 
cross - 

s+ poini 




cn 


N 


\ 


, 1 __ 












1/1 
o 




X» X' 


\^\ 


^ 


































T3 

1 6 ° 
















^ 


^ 






^7b 
























Figure 
witti 
and 




c 

IT 


3 


C 


3 




1 




c 




c 


5 


c 



;;hCa arr no. L5F0i 



Fig. 18a, b 










^cO 










o 
o 




O 








_o 






E 

E 




o 




X 


— 0) 


CO 




o 
£ 


^ CD 








^CiZ 




•J^ 


o 


^£ 




Y- 


(/I 


o 




a) 


UO 




r" 


i! 


c*- 








:ac 


o 




0) 




^T 




p 


1 ~^" 






u 








V 


<U (U 






> 


C 1- 






<. 


C O 

o 


O 




s 


"ormed ch 
in curves 



X 

O 

E 

iG 



























\ 






















\ 


\^ 






- '- ^ 
















W 






















c 


\, 




-C 
















D 

cn 




\ 


\ 
















in 
O 




xS 


"< 


\ 














u 










^^ 


























-^ 


























^^ 




c 


z> 


C 


D 


c 


D 


C 


D 


C 


3 


C 



\ o 



u 
O 



O 



c 

o 

"*- D:i= 

° I .b 

F^ o 

\f) ■ {T> 

r! ' 

> — ul 

•" H ^ 

J) ^ o 
£ \^ 

'*- ^'- 

O CPO 
C ,^ 0) 



.— 1_ — 

o *" 
Qroc 

^ cn4f 



NACA ARR No. L5F01 



Fig. 19 



60 



50 



40 



ksi 

30 



20 



\o 





bw 










^i^' 


20 18 16 14 






^VvX 


\xr\ 






24 k 


\\\N 


\\V\ 






26 Ln 


s\\\ 




\ 




2eL N 

30 L\ 


\\\ 


v$w 


^\ 






\\\ 


\ \ N. 


k\\\ 




-kN 




\ XNX 


^NN\ 




36. X 


\\\\ 


\\\ 


$$^ 




38 


^N 


\\\N 


\ \ \ 


XV 




40 V \ 


SSNa 


\\\ 


\ \N 




^*K 


^ 


Xv\ 






N 


^ 


Si 


i 








-^ 





'w 



.8 I.O 

NATIONAL ADVISORY 
COMMinEE FOR AESONAUTICS 



Rgure 19. - Design chart for a^p ^o^ formed Z45-T 
alurninum - alloij Z- and channel -sec+ion colunnns that 
develop local instabilittj loaded in the with -grain 



direction 



CTq^ 



= 44 ksi. 



NACA ARR No. L5F01 



Fig. 20 



60 



50 



40 



30 



ksi 



20 



10 





. 1 








t 

20 


18 16 15 




^."^ 


^^^. 




22 


\ \ N 


<:^^ 


V 




24 


\\N 


\Vv 


^ 




26 


s\ \ 


\J\\ 


nN^. 




30 




>$$ 


■•n^^V^^>^ 




34 


^^^^ 


>^\ 


^^^;;^^ 




38 


=^ 


^ 


fc 


- 






NATIONAL / 
COMMinEE FOR 


DVISORY 
\ERONAUTICS 



.6 



.S 



1.0 



'W 



Figure 20.- Design chart for CT>„ax for formed 24S-T 
aluminum - alloy Z- section columns that develop local 
instability loaded in the with- groin direction *, 0'j.ys44ksi 



NACA ARR No. L5F01 



Fig. 21 



60 



50 



40 



30 



'max 



ksi 



20 



lO 



o 







20 


Id 


6 15 






\^ 




n\\ 






zek \ 


\\ 


^\^ 


^^^^^ 


. 






\" 






^^Jx 




K\ 


\ 


\\ 


""v \;^ 


^^^:>^ 




"^ 


V \ 


\\ 




^^ 




36 


^ 


^ 


C:\ 


^^^$^ 


\::^ 




42 








^ 










V 










NATIONAL A[ 


VISORY 










;OMMinEE FOR A 


;ronautics 






a 



i.o 



Figure Zl. - Design chart for o-j^qx for formed Z45-T 
aluminum - alloy channel - section columns that develop 
locol instability loaded in the with -grain direction j 



<Tcy = 44 ksi 



I 



UNIVERSITY OF FLORIDA 



3 1262 08106 493 2 



UNIVERSITY OF FLORIDA 
DOCUMENTS DEPARTMENT 
120 MARSTON SCIENCE LIBRARY 
RO. 30X117011 
GAINESVILLE. FL 32611-7011 USA